1. Field of the Invention
The present invention relates to a mobile communication system, and more particularly to an apparatus and method for estimating a decision boundary of a specific signal to which a higher order modulation scheme is applied, in a receiver for use in the mobile communication system.
2. Description of the Related Art
Mobile communication systems have evolved from typical voice-centered mobile services to high-speed packet transmission services to make it possible to transmit not only voice data but also high-speed packet data. The 3rd Generation Partnership Project (3GPP2) and the 3GPP2 for use in the third-generation mobile communication standard have recently proposed a variety of high-speed packet communication systems. For example, a High Speed Downlink Packet Access (HSDPA) standardization is in progress in the 3GPP, and a Evolution Data and Voice (1xEV DV) standardization is in progress in the 3GPP2.
Typically, a digital signal transmission system is superior to an analog signal transmission system because it is less sensitive to noise, has lower distortion, and has higher transmission efficiency as compared to the analog signal transmission system. However, the digital signal transmission system has a disadvantage in that it requires a wider bandwidth and higher system complexity as compared to the analog signal transmission system. As a variety of circuit technologies have been developed, the digital signal transmission system has been widely used in a variety of communication schemes because it generates less errors and has higher reliability compared to the analog signal transmission system.
A representative example of such a digital modulation/demodulation technique capable of transmitting two-bit input signals as a single signal is a Quadrature Phase Shift Keying (QPSK) scheme. The QPSK scheme transfers an odd bit of input bits to an In-phase (I)—channel, and transfers an even bit of the input bit to a Quadrature (Q)—channel, such that a specific value ‘0’ is changed to ‘−1’, and other value ‘1’ remains. In this case, the input bits each are matched with a predetermined phase and amplitude to create modulated signals. These modulated signals each are typically called a symbol.
However, in order to implement high-speed data transmission for the aforementioned wireless communication system, there has recently been proposed a higher-order modulation scheme such as an M-Quadrature Amplitude Modulation (M-QAM) scheme capable of improving a data transfer rate.
The M-QAM scheme matches input bits with a plurality of phases and amplitudes to create modulation signals, and is classified into a variety of modulation schemes (for example, 4 Quadrature Amplitude Modulation (QAM), 16QAM, 32QAM, 64QAM, 128QAM, and 256QAM, etc.) according to a modulation rate.
The 16QAM scheme included in the M-QAM scheme will hereinafter be described with reference to FIG. 1. It should be noted that the 16QAM scheme has been disclosed for illustrative purposes and therefore the present invention can also be applicable to the remaining M-QAM schemes other than the 16QAM scheme.
FIG. 1 is a diagram illustrating a constellation of a conventional 16QAM scheme.
Referring to FIG. 1, an input signal of 4 bits includes 16 values (i.e., 24=16) ranging from ‘0000’ to ‘1111’, such that the 16 values can be mapping-processed on 16 positions contained in a complex plain. Two preceding bits from among the four bits are separated from each other according to individual quadrants contained in a complex plain, and two following bits from among the four bits are separated from each other according to four fields partitioned in a prescribed quadrant. For example, two preceding bits of all symbols contained in a first quadrant of the complex plain are assigned ‘00’, the first quadrant is divided into four fields, and these four fields are respectively assigned ‘00’, ‘01’, ‘10’, and ‘11’ each serving as two following bits.
In this manner, a signal modulated into 16 symbols is transmitted to a receiver. The receiver demodulates the signal composed of 16 symbols into corresponding bits according to the amplitude and phase of individual symbols. Individual symbol values are determined on the basis of a specific position having an amplitude of 2A. For example, if a Q-channel amplitude is higher than the amplitude of 2A in the first quadrant of the complex plain, symbol values ‘0001’ and ‘0011’ are separated from each other on the basis of a specific position having an I-channel amplitude of 2A. In this case, such a boundary value (e.g., 2A) capable of distinguishing a plurality of symbols from each other is called a decision boundary.
In case of transferring the aforementioned symbols over a wireless channel environment, the symbol signals incur considerable distortion due to signal fading or noise.
Therefore, the signal mapping-processed with the aforementioned symbols may be unexpectedly higher than the decision boundary such that it could be mistaken for wrong symbols. A reception error rate is determined according to the number of wrong symbols.
Therefore, the higher-order modulation scheme such as the 16QAM scheme can enhance a data transfer rate, but it has a disadvantage in that it must estimate individual phases and amplitudes of plural symbols in order to allow the receiver to perform symbol decision whereas the QPSK scheme can discriminate between such symbols on the basis of only the phase. Therefore, there must be newly developed a technique capable of estimating more reliable and reasonable decision boundaries in consideration of signal distortion caused by channel environments.
As described above, a demodulator of the receiver adapts the decision boundary to perform soft or hard decision of symbols, and it is preferable for information related to the demodulator to be estimated from a reception signal.
Provided that there are numerous transmission symbols, they are stochastically and equally distributed on the constellation shown in FIG. 1. There has recently been proposed a variety of schemes for estimating such a decision boundary using the aforementioned characteristic, for example, a first scheme for calculating a mean absolute value by accumulating absolute values of reception symbols during a predetermined period of time, and an unbiased estimation scheme considering noise dispersion to remove a bias component caused by noise, etc.
Typically, the first scheme for calculating a decision boundary of reception symbols by acquiring a mean value of absolute values of reception signals is effectively used in the case of a high Signal to Noise Ratio (SNR), and the unbiased estimation scheme is effectively used in the case of a low SNR.
The aforementioned estimation schemes are different in terms of performance according to the SNR. Provided that a decision boundary estimation process is performed on the condition that a sufficient accumulation period has been provided, the first scheme and the unbiased estimation scheme converge on an ideal decision boundary contained in the symbol constellation of symbols.
However, the aforementioned schemes must accumulate symbols for a long period of time to estimate the decision boundary, such that they require a long processing-time to accumulate the reception symbols. In addition, if the reception symbols are unevenly created on the constellation, the aforementioned schemes may cause undesired performance deterioration.
For example, the above scheme for acquiring an amplitude level of a reception symbol by averaging absolute values of reception signals is applied to the High Speed Downlink Packet Access (HSDPA), one of the high-speed data transmission schemes, and problems associated with this exemplary scheme will hereinafter be described in detail.
First of all, the HSDPA, one of the high-speed data transmission schemes, will hereinafter be described.
The HSDPA scheme is a general term of a prescribed data transmission scheme including an High Speed-Downlink Shared Channel (HS-DSCH) serving as a downlink data channel for supporting high-speed downlink packet data transmission in a Universal Mobile Terrestrial System (UMTS) and control channels associated with the HS-DSCH. There have recently been proposed an Adaptive Modulation and Coding (AMC) scheme, a Hybrid Automatic Retransmission Request (HARQ) scheme, and an Fast Cell Select (FCS) scheme to support the HSDPA scheme, and their detailed description will herein be omitted because they have no connection with the present invention.
The HSDPA scheme transmits data over a High-Speed Physical Downlink Shared CHannel (HS-PDSCH) functioning as a traffic channel, and at the same time transmits data over a (Physical Common PIlot CHannel) (PDPICH) functioning as a pilot channel. The HS-PDSCH can transmit data, and can also transmit such data according to 16QAM and QPSK schemes. For the purpose of simplicity, it is assumed that data transmission is performed using only the 16QAM scheme.
The PCPICH is a pilot channel, and is adapted to estimate a phase of a reception signal by transmitting prescribed symbols (e.g., an operation for continuously transmitting signals of ‘1’) between a transmitter to a receiver.
In the meantime, a narrow-band modulation signal dk of a k-th HS-PDSCH from among a plurality of HS-PDSCHs can be represented by the following Equation 1:
                                          d            k                    ⁡                      (            t            )                          =                              ∑                          -              ∞                        ∞                    ⁢                                          ⁢                                    A              d                        ·                                          g                k                            ⁡                              (                i                )                                      ·                          exp              ⁡                              [                                  j                  ⁢                                                                          ⁢                                                            Φ                      k                                        ⁡                                          (                      ⅈ                      )                                                                      ]                                      ·                          u              ⁡                              (                                                      t                    /                                          T                      s                                                        -                  ⅈ                                )                                                                        [                  Equation          ⁢                                          ⁢          1                ]            
where, gk(i)=√{square root over (Ik2+Qk2)}, |I|,|Q|ε{A,3A},
                    Φ        k            ⁡              (        i        )              =                  tan                  -          1                    ⁢                        Q          k                          I          k                      ,and u(t) is a unit step function. As is well known in the art, the unit step function u(t) can be represented by the following Equation 2:
                              u          ⁡                      (            t            )                          =                  (                                                                      1                  ,                                                                                                  for                    ⁢                                                                                  ⁢                    0                                    ≤                  t                  <                  1                                                                                                      0                  ,                                                                              otherwise                  ⁢                                                                                                                      )                                                                [                  Equation          ⁢                                          ⁢          2                ]            
Referring to Equations 1 and 2, Ad is a constant where an amplitude of a transmission signal is reflected, gk is an amplitude of a corresponding symbol, and Φk(i) is a phase of the corresponding symbol.
Spread code waveform associated with the k-th HS-PDSCH from among a plurality of HS-PDSCHs is represented by the following Equation 3:
                                          c            k                    ⁡                      (            t            )                          =                              ∑                          -              ∞                        ∞                    ⁢                                    exp              ⁡                              [                                  j                  ⁢                                                                          ⁢                                                            Φ                      k                                        ⁡                                          (                      ⅈ                      )                                                                      ]                                      ·                          u              ⁡                              (                                                      t                    /                                          T                      c                                                        -                  ⅈ                                )                                                                        [                  Equation          ⁢                                          ⁢          3                ]            
where, Φk is a complex channelization code, and is denoted by Φk(i)ε{νπ/2+π/4; ν=0,1,2,3}.
The PCPICH serving as a pilot channel for channel estimation is represented by the following Equation 4:
                                          d            cpich                    ⁡                      (            t            )                          =                              ∑                          -              ∞                        ∞                    ⁢                                    A              p                        ·                          g              cpich                        ·                          exp              ⁡                              (                                  j                  ⁢                                                                          ⁢                                      π                    /                    4                                                  )                                      ·                          u              ⁡                              (                                                      t                    /                                          T                      cpich                                                        -                  ⅈ                                )                                                                        [                  Equation          ⁢                                          ⁢          4                ]            
Equation 4 is denoted in a manner similar to the traffic modulation signal of the HS-PDSCH shown in Equation 1. As can be seen from Equation 4, the PCPICH continuously transmits specific symbol signals, such that the reference character ‘g’ indicative of an amplitude and the reference character ‘Φk’ indicative of a phase are denoted by constants, respectively. For example, ‘g’ may be set to ‘gcpich’ and ‘Φk’ may be set to π/4. The other reference character ‘Ap’ is a constant for reflecting an amplitude of a transmission signal associated with a pilot signal in the same way as in ‘Ad’.
Similarly to the spread code waveform associated with the HS-PDSCH, spread code waveform of the PCPICH is denoted in a manner similar to the traffic modulation signal, and different code values are assigned to individual channels. In this case, codes assigned to individual channels are orthogonal codes as well known in the art. In conclusion, the spread code waveform of the PCPICH can be represented by the following Equation 5:
                                          c            cpich                    ⁡                      (            t            )                          =                              ∑                          -              ∞                        ∞                    ⁢                                    exp              ⁡                              [                                  j                  ⁢                                                                          ⁢                                                            Φ                      cpich                                        ⁡                                          (                      ⅈ                      )                                                                      ]                                      ·                          u              ⁡                              (                                                      t                    /                                          T                      cpich                                                        -                  ⅈ                                )                                                                        [                  Equation          ⁢                                          ⁢          5                ]            
where, gcpich is an amplitude of the PCPICH, and Tcpich is a symbol period.
Provided that one HS-PDSCH and one PCPICH are transmitted over a transmitter, a transmission signal r(t) can be represented by the following Equation 6:r(t)=d1(t)·c1(t)+dcpich(t)·ccpich(t)  [Equation 6]
With reference to Equation 6, the modulation signal di(t) of the HS-PDSCH is multiplied by the channelization code waveform c1(t), thereby creating a signal denoted by d1(t)·c1(t). The modulation signal dcpich(t) of the PCPICH is multiplied by the channelization code waveform ccpich(t), thereby creating the other signal denoted by dcpich(t)·ccpich (t). If the signal denoted by d1(t)·c1(t) is added to the other signal denoted by dcpich(t)·ccpich(t), there is provided the resultant signal r(t) transferred over the transmitter.
In this case, if the signal r(t) transferred over the transmitter is received in the receiver, it is affected by multi-path fading and noise, such that it can be represented by the following Equation 7:r(t)=h(t)·[d1(t−τ1)·c(t−τ1)+dcpich(t−τ1)·c(t−τ1)]n(t)  [Equation 7]
where, h(t) is a complex channel gain, τ1 is a predetermined time delay, and n(t) is a noise component added to the reception signal r(t). Typically, n(t) indicates a noise component having spectrum density of No/2.
The reception signal r(t) shown in Equation 7, that has been affected by the fading and noise and then transmitted to the receiver, is adapted to estimate a channel environment in the receiver, such that an original transmission signal is effectively demodulated.
The receiver will hereinafter be described with reference to FIG. 2.
Referring to FIG. 2, the despreader 100 despreads the reception signal r(t). In this case, the output signal z(n) of an n-th symbol that has been despread by the despreader 100 and then transmitted to the channel compensator 120 is represented by the following Equation 8:
                              z          ⁡                      (            n            )                          =                              1                          T              s                                ⁢                                    ∫                                                T                  ⁢                                                                          ⁢                  s                                +                                  τ                  ^                                                                                                  (                                          n                      +                      1                                        )                                    ⁢                  T                  ⁢                                                                          ⁢                  s                                +                                  τ                  ^                                                      ⁢                                                            r                  ⁡                                      (                    t                    )                                                  ·                                                      C                    *                                    ⁡                                      (                                          t                      -                                              τ                        ^                                                              )                                                              ⁢                                                          ⁢                              ⅆ                t                                                                        [                  Equation          ⁢                                          ⁢          8                ]            
With reference to Equation 8, the despread output signal z(n) can be calculated by performing a convolution operation between the reception signal r(t) and the channelization code during a predetermined symbol period Ts. In this case, ‘*’ is a complex conjugate, and {circumflex over (τ)} is an estimated time delay.
The PCPICH signal transferred to perform channel estimation is despread by the despreader 100, and is then transmitted to the channel estimator 110. The PCPICH signal Zcpich(n) having been despread and transmitted to the channel estimator 110 can be represented by the following Equation 9:
                                          z            cpich                    ⁡                      (            n            )                          =                              1                          T              cpich                                ⁢                      ∫                                                            r                  ⁡                                      (                    t                    )                                                  ·                                                      C                    cpich                    *                                    ⁡                                      (                                          t                      -                                              τ                        ^                                                              )                                                              ⁢                                                          ⁢                              ⅆ                t                                                                        [                  Equation          ⁢                                          ⁢          9                ]            
where, zcpich(n) is an output value of the n-th symbol of the PCPICH serving as a pilot channel.
In this case, provided that channel estimation is ideally performed and no noise occurs, ĥ(n) created by transmitting the n-th symbol output signal zcpich(n) of the PCPICH over the channel estimator 110 can be represented by the following Equation 10:ĥ(n)=Ap·h(n)  [Equation 10]
where, Ap is a constant indicative of an amplitude of a transmission signal associated with a pilot signal, and h(n) is a complex channel gain.
ĥ(n) generated from the channel estimator 110 performs channel estimation on a reception signal generated from the despreader 100. Specifically, the reception signal is affected by the channel environment according to the channel environment condition having been estimated by the channel estimator 110, such that a distortion component can be compensated. For example, provided that the reception signal causes an undesired phase variation of θ over a wireless environment, it can be restored to the original transmission signal by compensating with a phase value of −θ. The above signal ĥ(n) is applied to the channel compensator 120 and the decision boundary estimator 130. The reception signal z(n) having been despread by the despreader 110 as shown in Equation 8 performs a predetermined operation on the channel estimation value ĥ(n), thereby creating a channel-compensated output signal.
The output value d(n) having been channel-compensated by the channel compensator 120 can be represented by the following Equation 11:d(n)=ĥ*(n)·z(n)=∥h(n)∥2ApAd·g(n)[Equation 11]
A predetermined scalar product operation between a complex conjugate of the signal ĥ(n) generated from the channel estimator 110 and the output value z(n) of the despreader 100 is performed, resulting in a channel-compensation signal. With reference to Equation 11, channel distortion contained in the channel-estimation signal is normally compensated, such that the channel-estimation signal is composed of only four signals, i.e., h(n), Ap, Ad and g(n).
The demodulator 140 determines a mapping position contained in the constellation in association with the n-th symbol signal d(n) generated from the channel compensator 120. In the meantime, provided that the reception signal is an ideal signal having no distortion over a wireless channel, it can be correctly determined by a specific decision boundary (e.g., 2A).
However, since the reception signal is affected by real-time distortion created over a wireless channel, it is preferable for a substantial decision boundary to be adaptively determined according to the channel environment.
Therefore, upon receiving the channel-compensation reception signal d(n) from the channel compensator 120, the decision boundary estimator 130 preferably estimates a decision boundary in consideration of channel environment. The demodulator 140 modulates reception signal d(n) into bit values according to the decision boundary estimated by the decision boundary estimator 130. For example, in case of the 16QAM scheme, the reception signal d(n) is modulated into four bits for every symbol.
Bit data demodulated by the demodulator 140 is decoded by the decoder 150. The UMTS system typically adapts a turbo decoder as a decoder.
The decision boundary estimator will hereinafter be described with reference to FIG. 3.
FIG. 3 is a detailed block diagram of the decision boundary estimator 130 shown in FIG. 2.
Referring to FIG. 3, a complex signal shown in Equation 11 has been generated from the channel estimator 120 shown in FIG. 2, and is classified into an In-phase component and a Quadrant-phase component to perform a real-number operation. In more detail, the In-phase component contained in the output signal of the channel compensator 120 is transmitted to a first absolute value calculator 200, and the Quadrant-phase component is transmitted to a second absolute value calculator 220. In the meantime, the output signal of the channel estimator 110 is a channel gain denoted by Equation 10, and is transmitted to a third absolute value calculator 240.
Upon receiving the channel-compensated output signals (i.e., In-phase and Quadrature-phase components) from the channel compensator 120, the first and second absolute value calculators 200 and 220 calculate individual absolute values of the received signals, and the first accumulator 210 and the second accumulator 230 perform an accumulation and dump operation on the calculated absolute values.
The signals having been applied to the first and second absolute value calculators 200 and 220 each include a real part and an imaginary part, and are processed while being classified according to the real part and the imaginary part. However, the signals are equivalent to the complex symbol expression, such that the same signal processing step is applied to them. Therefore, the first accumulator 210 is adapted to accumulate the absolute value of N signals having the In-phase component, and the second accumulator 230 is adapted to accumulate the absolute value of N signals having the Quadrature-phase component. The absolute-value accumulated signals created from the first and second accumulators 210 and 230 are added to each other in the adder 260, this value is divided by 4 using the ¼ divider 270, and a resultant signal is transmitted to another divider 280.
In the meantime, if the output signal of the channel estimator 110 is transmitted to the third absolute value calculator 240, the third absolute value calculator 240 numerically squares an absolute value of the received signal, and the squared signal is transmitted from the third absolute value calculator 240 to the third accumulator 250. The third accumulator 250 accumulates the received signal by N symbols, and transmits the accumulated signal Y to the divider 280.
A division operation between the two signals X and Y applied to the divider 280 is performed. In more detail, the divider 280 divides the sum value X created by accumulating the absolute value of the complex signal by the output value Y of the channel estimator 110.
In this case, the signal is generated from the channel compensator 120, and is then transmitted to the divider 280 after accumulating its own absolute value. This signal can be represented by the following Equation 12:
                                                                                                              ∑                                          n                      =                      1                                        N                                    ⁢                                                                          ⁢                                                                                                                                                                                        h                            ⁡                                                          (                              n                              )                                                                                                                                2                                            ·                                              A                        d                                            ·                                              A                        p                                            ·                                                                                                Re                          ⁢                                                      {                                                          g                              ⁡                                                              (                                n                                )                                                                                      }                                                                                                                                                                                          +                                                                                                          ∑                                      n                    =                    1                                    N                                ⁢                                                                  ⁢                                                                                                                                                                        h                          ⁡                                                      (                            n                            )                                                                                                                      2                                        ·                                          A                      d                                        ·                                          A                      p                                        ·                                                                                        Im                        ⁢                                                  {                                                      g                            ⁡                                                          (                              n                              )                                                                                }                                                                                                                                                                                                4                            [                  Equation          ⁢                                          ⁢          12                ]            
With reference to Equation 12, the output signal of the channel compensator 120 is divided into a real part and an imaginary part, and its absolute value is calculated while being classified according to the real part and the imaginary part. The calculated absolute value is accumulated during a predetermined time corresponding to N symbols, and the accumulated result is divided by 4.
In the meantime, an output signal of the channel estimator 110 is applied to the decision boundary estimator 130, an absolute value of the output signal is accumulated, and the accumulated result is applied to the divider 280. In this case, the signal applied to the divider 280 is represented by the following Equation 13:
                              ∑                      n            =            1                    N                ⁢                                                                        h                ⁡                                  (                  n                  )                                            ·                              A                p                                                          2                                    [                  Equation          ⁢                                          ⁢          13                ]            
With reference to Equation 13, an absolute value of ĥ(n) denoted by Equation 10 is squared, the squared result is accumulated during a predetermined time corresponding to N symbols, and the accumulated result is transferred to the divider 280 in such a way that the signal denoted by Equation 13 is created.
Finally, the divider 280 divides the signal denoted by Equation 12 by the other signal denoted by Equation 13. That is, the divider 280 performs division operation on the output signal of the decision boundary estimator 130, such that the last output signal of the decision boundary estimator 130 can be represented by the following Equation 14:
                                          θ            ^                    1                =                                            A              d                                      A              p                                ⁢          A                                    [                  Equation          ⁢                                          ⁢          14                ]            
As described above, considering the fact that the absolute value of mean amplitudes of the real and imaginary parts converge on a specific value of 2A after the lapse of a long period of time, the decision boundary estimator 130 normalizes the sum of individual absolute values with a channel gain, and divides the normalized value by 4. The normalized value is divided by 4 because the sum of a mean value (A+3A)/2 of the real part and a mean value (A+3A)/2 of the imaginary part converges on a specific value of 4A on the condition that the value of N is sufficiently high and creation frequencies of all symbols are equal to each other.
As previously shown in FIG. 2, the output signal of the channel compensator 120 and the output signal of the decision boundary estimator 130 are transmitted to the demodulator 140, and are adapted to set up a reference amplitude for determining a symbol. Therefore, a soft-decision process of the output value of the channel compensator 120 is performed by the output value of the decision boundary estimator 130.
For reference, there are two quantization methods for symbols received over the channel, i.e., a hard decision method and a soft decision method. In more detail, data received over the channel is slightly different from a predetermined data value modulated in a transmission step. The hard decision method determines the reception data using only two levels ‘1’ and ‘0’ according to a predetermined reference. The soft decision method converts a baseband signal into digital data having a specific level of 2n using a soft-decision threshold value predetermined by an N-bit Analog-to-Digital Converter (ADC). There is a little difference in a coding gain according to a quantization method of the demodulated data. For example, throughput performance of a 16-level soft decision method is superior to that of the hard decision method by about 2 dB, such that most digital communication systems mainly prefer the soft decision method to the hard decision method.
Provided that the aforementioned conventional decision boundary {circumflex over (θ)}1, and the output signal z(n) are adapted as input signals and a simple metric method is adapted to calculate a soft Long Likelihood Ratio (LLR), a signal composed of 4 bits is created by demodulating a predetermined symbol. This 4-bit signal can be represented by the following Equations 15˜18:Λ0(z(n))=In  [Equation 15]Λ1(z(n))=Qn  [Equation 16]Λ2(z(n))=2·A−|In|  [Equation 17]Λ3(z(n))=2·A−|Qn|  [Equation 18]
Referring to the above Equations 15˜18, Λi(z(n)) indicates an LLR of an i-th bit of the n-th symbol. In more detail, Equation 15 indicates a first bit from among the output bits (i.e., 4 bits) associated with a single symbol, and Equation 18 indicates the last bit from among the four bits.
In this case, Equation 15 and Equation 16 indicate two preceding bits from among the above four bits, respectively, such that they are adapted to determine a quadrant of a complex plain. Equation 17 and Equation 18 indicate two following bits from among the four bits, such that they are adapted to discriminate among four fields of a predetermined quadrant. In this case, ‘In’ indicates an In-phase component of the n-th symbol, and is represented by the following Equation 19. ‘Qn’ indicates a Quadrature-phase component of the n-th symbol, and is represented by the following Equation 20.In=Re{z(n)}  [Equation 19]Qn=Im{z(n)}  [Equation 20]
Since ‘In’ and ‘Qn’ are channel-compensated signals, Λ2 can be represented by the following Equation 21 using its corresponding gain and an estimation value {circumflex over (θ)}1, of a reference level, and Λ3 can be represented by the following Equation 22 using its corresponding gain and the estimation value {circumflex over (θ)}1 of the reference level.Λ2(z(n))=2·{circumflex over (θ)}1·Ap2·∥h(n)∥2−|In|  [Equation 21]Λ3(z(n))=2·{circumflex over (θ)}1·Ap2·∥h(n)∥2−|Qn|  [Equation 22]
Finally, the aforementioned four-bit output signals associated with 16QAMs of the Equations 15, 16, 21, and 22 are applied to the decoder 150, and are then decoded by the decoder 150.
As described above, the scheme for averaging the accumulated absolute values of reception symbols and the other scheme for estimating the decision boundary using a mean accumulation value of the squared absolute value are different in performance according to a reception SNR, however, they are all designed on the assumption that transmission symbols are evenly distributed on the constellation and are then transmitted to a target object. Therefore, the conventional decision boundary estimator necessitates numerous reception symbol samples (e.g., symbols corresponding to about one packet), such that it unavoidably create an unnecessary time delay as long as a prescribed accumulation time needed for the decision boundary estimation process. Furthermore, the conventional decision boundary estimator unexpectedly incurs performance deterioration depending on the SNR.
In conclusion, the scheme for averaging the accumulated absolute value of reception symbols and the other scheme for adapting the square of the mean accumulation value each incur an undesired time delay corresponding to the accumulated samples, such that it is difficult for either one of them to be applied to hardware (e.g., an interference canceller for requesting a real-time processing) to be processed at a high speed, for example, an interference canceller for requesting a real-time processing.